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The strong pump beam at c is undepleted. i.e. The weak signal beam at a is amplified. An idler beam at b is generated A pump beam photon breaks up into a signal photon and idler photon OPA: Undepleted Pump Approximation

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Clearly the functional behavior depends on the sign of 2. 1.The behavior near and on phase match ( 2 >0) is exponential growth 2.When 2 <0, the behavior is oscillatory. 3.Using the boundary condition

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z For this difference frequency process, the larger the intensity gain coefficient 2, the broader the gain bandwidth! This is contrast to SHG (i.e. sum frequency case) in which the bandwidth narrows with increasing intensity Exponential Gain Coefficient

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z No gain! Notes: 1.For large, low level oscillations still exist, but are too small to be seen 2.The zero level is different for. 3.For there is no signal gain, just energy exchange with the idler as shown above.

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OPA Solutions with Pump Depletion Note: 1.This amplifier response is periodic in distance and pump power. 2.Therefore there is no saturation as with other amplifiers. 3.The gain is exponential, but only over a finite range of length. 4.For small distances the signal growth is not exponential although the idler growth is!

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Optical Parametric Oscillators (OPOs) OPOs are the most powerful devices for generating tunable radiation efficiently. Put a nonlinear gain medium in a cavity, noise at a and b is amplified. By using a cavity, the pump is depleted more efficiently. Using a doubly resonant cavity (resonant at both the idler and the signal), the threshold for net gain is reduced substantially. Triply resonant cavities (also resonant at the pump frequency) have been reported, but their stability problems have limited their utility and commercial availability Assume that pump is essentially undepleted on a single pass through the cavity Singly Resonant Oscillator Have to deal with cavity modes at signal frequency Doubly Resonant Oscillator Cavity modes at both signal and idler frequency need to be considered (2) c b a

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- In addition, since the mirrors are coated for high reflectivities at b and a, they accumulate phase shifts of 2k b L and 2k a L respectively after a single round trip inside the cavity. Linear phase accumulation Reflection Steady state after one round trip

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Singly Resonant OPO (SRO) Cavity is resonant at only one frequency, usually the desired signal ( a ) R a 1 R b 0 Threshold much higher for SRO than for DRO e.g. The threshold for the previously discussed LiNbO 3 case is 1 MW/cm 2 Stability of Singly Resonant OPO If the cavity drifts, the output frequency drifts with it, no large mode hops occur. Frequency hops will be just the mode separation.

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OPO Output At threshold, gain=loss. If I( c ) > I th ( c ), input photons in excess of threshold are converted into output signal and idler photons One pump photon is converted into one signal and one idler photon. How much comes out of OPO depends on the mirror transmission coefficients slope efficiency